For describing the background of the invention, particular reference is made to the following publications:    [1] V. R. Fuchs et al. in “Health Aff.” 20: 30-42 (2001);    [2] D. I. Hoult. Sensitivity of the NMR experiment. In: D. M. Grant, R. K. Harris (eds.); Encyclopedia of Nuclear Magnetic Resonance, Vol. 7, pp. 4256-4266, Wiley, Chichester (1996);    [3] S. Zaroubi et al. in “Magn. Reson. Imaging” 18: 59-68 (2000);    [4] J. B. Weaver et al. in “Magn. Reson. Med.” 21: 288-295 (1991);    [5] U.S. Pat. No. 6,741,739 B1;    [6] S. G. Chang et al. in “IEEE Trans. Image Proc.” 9: 1522-1531 (2000);    [7] C. S. Anand et al. in “Magn. Reson. Imaging” 28: 842-861 (2010);    [8] US 2014/0212015 A1;    [9] E. T. Olsen et al. in “Proc. SPIE 2491, Wavelet Applications II” 829-839 (1995);    [10] R. M. Henkelman et al. in “Med. Phys.” 12: 232-233 (1985);    [11] A. J. den Dekker et al. in “Phys. Medica” 30: 725-741 (2014); and    [12] D. K. Müller et al. in “J. Magn. Reson.” 230: 88-97 (2013).
Magnetic resonance imaging (MRI) is a standard biomedical imaging modality and has been considered (together with computed tomography) “the most important medical innovation” during the past decades in a 2001 survey among leading US American physicians [1]. However, MRI has also an inherently low sensitivity: Considering three-dimensional (3D) proton (1H) MRI of the human brain with a nominal isotropic resolution of 1 mm and at a typical static magnetic field strength of B0=1.5 T used in diagnostic MRI, the individual contribution from a single image voxel (i.e., a volume of 1 μl) to the signal amplitude is of the order of only 10 nV [2]. Thus, despite its success, MRI is often limited by a low signal-to-noise ratio (SNR). The problem of an inherently low sensitivity is becoming increasingly important when applying MRI techniques, in which a certain preparation of the spin system and spatial encoding by the imaging pulse sequence is used to achieve a quantitative parametric characterization of the object under investigation (e.g., a tissue or an organ or a whole organism). Quantitative MRI (qMRI) aims to derive voxel-by-voxel well-defined biophysical, biochemical, or physiological parameters from MR images or 3D MR data sets instead of merely examining them by visual inspection. Here, the image intensity is often reduced to a very low level, which is, however, mandatory in order to retrieve the quantitative information. Examples of (semi-)quantitative mapping approaches include relaxographic imaging, quantitative magnetization transfer imaging (qMTI), diffusion-weighted imaging (dMRI), arterial spin labeling (ASL) or dynamic susceptibility contrast (DSC) imaging, for mapping tissue perfusion, or vascular space occupancy (VASO) for mapping tissue blood volume. Similarly, functional MRI (fMRI) of the brain aims at the detection of dynamic signal changes (e.g., expressed as percent of a baseline level) related to neuronal activation upon application of a stimulus or performance of a task.
To address limitations of the low SNR in magnetic resonance, several strategies are being employed for improving the signal amplitude, such as the use of higher static magnetic fields or hyperpolarization techniques. However, such strategies are demanding and expensive regarding the necessary hardware. Furthermore, the gain achieved by a higher magnetic field is only moderate (approximately linear increase with B0) whereas the applicability of hyperpolarization is rather limited to specific applications. Alternatively and additionally the SNR can be improved by reducing the image noise, for example, by using improved radiofrequency (RF) receivers designed as an array of small individual coils. Appropriate choice of the size of the array elements reduces the effective size of that part of the sample that acts as a noise source, which is, however, limited by the overall size of the object to be imaged.
Besides hardware solutions for improved SNR, noise in the final image can be reduced through averaging, that is, the repetitive measurement of the data under identical conditions and subsequently co-adding them. The SNR gain results from a linear buildup of the (coherent) signal (subsequently also referred to as ‘information’) with the number of averages, Mav, whereas random noise only grows proportional to √{square root over (Mav)}; hence, SNR improves with √{square root over (Mav)}. This method requires an identical contrast for all images that are supposed to be averaged and is time consuming (e.g., to double the SNR requires four times the number of scans). In particular, while averaging of all data, e. g. from an image series acquired with variation of specific acquisition parameters to extract a quantitative property of the tissue after application of a fitting procedure, would lead to a final dataset with high SNR, it would—at the same time—destroy all underlying information about the parameter to be extracted or the time-dependence of the dynamic experiment, and hence, traditional averaging has substantial limitations. Similarly, smoothing of the images unavoidable leads to a smearing of contrast and thus effectively reduces the image resolution.
While averaging does not involve further manipulation of the acquired data than a simple voxel-by-voxel summation and division by Mav to normalize to a constant signal level, another class of methods aims at reducing the noise by application of digital filters. Here, some contributions to an image are identified as originating from noise through the application of suitable filtering techniques and are subsequently removed or reduced. This procedure is synonymously called ‘noise filtering’, ‘noise suppression’, or ‘denoising’. In many of these denoising methods, images are expanded in a functional basis that maintains their phase and amplitude distribution. By using a suitable functional basis, it is often possible to distinguish between the various contributions to the MRI data and to filter the noise [3]. Particular examples of denoising methods, which are also suitable to imaging in general, employ the discrete wavelet transform [4]. Since then, a plethora of algorithms for the adaptation of wavelet-based denoising to MRI have been proposed.
Common methods for denoising in MRI employing wavelets are based on thresholding with a range of specific modifications and adaptations. Thresholding is typically performed in a way that parts of the image are assumed to contain only (or mostly) noise, for example, based on criteria of a low image intensity and/or characteristic high-frequency fluctuations. Such parts are then set to zero to effectively remove noise [5, 6]. More advanced methods comprise spatially-adaptive or phase-adaptive thresholding [7-9], for example, to better deal with spatial variations in image intensity. Such variations may occur in images reconstructed from multi-channel array coils.
A substantial disadvantage of these approaches is the suppression of information that result from weak and fine details of the imaged object that are hidden by overlaying noise contributions and, hence, misclassified as noise. Thresholding techniques typically aim at smooth images with intact sharp edges characterizing the object, and maximum SNR, which may come at the cost of a partial loss of finer details.